Binary to BCD Converter with Step-by-Step Visualization

Purpose of BCD

BCD represents each decimal digit separately with four bits. This lets a decimal display circuit handle one digit at a time. A BCD-to-seven-segment decoder reads a digit’s four bits and lights the matching display segments.

For example, decimal 45 has two digits: 4 and 5. BCD represents them as 0100 0101, while ordinary binary represents the whole number as 101101.

How to Convert Binary to BCD

1. Find the decimal value. Read the binary place values from right to left: 1, 2, 4, 8, and so on. Add only the values with a 1 bit.
2. Separate the decimal digits. Keep their left-to-right order.
3. Convert each digit to four bits. Use the weights 8, 4, 2, 1 from left to right. Choose the weights that add up to the digit. Write 1 for each weight you use and 0 for the others.
4. Join the groups. Keep a space between each four-bit group.

Example: 101101₂ → 45₁₀ → 0100 0101 in BCD.

The converter ignores spaces in your input. Leading binary zeros do not change the result. For zero, write 0000.

The converter calculates the full BCD result without rounding. You can watch the conversion steps for decimal values up to 99,999.

Binary to BCD Examples

Keep all four bits in each group, including leading zeros. In 8421 BCD, each group represents a digit from 0 to 9: 0000 to 1001. The groups 1010 to 1111 do not represent decimal digits.

Key terms